Fully Comprehensive Geometrically Non-Linear Dynamic Analysis
of Multi-Body Beam Systems with Elastic Couplings
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Abstract
This paper is concerned with the dynamic analysis of flexible,non-linear multi-body beam systems. The focus is on
problems where the strains within each elastic body (beam)
remain small. Based on geometrically non-linear elasticity
theory, the non-linear 3-D beam problem splits into either a
linear or non-linear 2-D analysis of the beam cross-section
and a non-linear 1-D analysis along the beam reference line.
The splitting of the three-dimensional beam problem into
two- and one-dimensional parts, called dimensional reduction,results in a tremendous savings of computational effort relative to the cost of three-dimensional finite element analysis,the only alternative for realistic beams. The analysis of beam-like structures made of laminated composite materials requires a much more complicated methodology. Hence, the analysis procedure based on Variational Asymptotic Method (VAM), a tool to carry out the dimensional reduction, is used here.The analysis methodology can be viewed as a 3-step procedure. First, the sectional properties of beams made of composite materials are determined either based on an asymptotic procedure that involves a 2-D finite element nonlinear analysis of the beam cross-section to capture trapeze effect or using strip-like beam analysis, starting from Classical Laminated Shell Theory (CLST). Second, the dynamic response of non-linear, flexible multi-body beam systems is simulated within the framework of energy-preserving and energy-decaying time integration schemes that provide unconditional
stability for non-linear beam systems. Finally,local 3-D responses in the beams are recovered, based on the 1-D responses predicted in the second step. Numerical examples are presented and results from this analysis are compared with those available in the literature